刚性球体在转动环形凹槽内的动力学行为

雷家睿, 韩润泽, 王柯人, 黄 敏, 赵芸赫, 马宇翰

doi:10.16854/j.cnki.1000-0712.210605

大学物理 >

2022 , Vol. 41 >Issue 10: 55

DOI: https://doi.org/10.16854/j.cnki.1000-0712.210605

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刚性球体在转动环形凹槽内的动力学行为

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1. 北京师范大学物理学系，北京100875；2. 四川省成都市新都一中铭章学院，四川成都610500；
3. 首都师范大学附属中学，北京100048；4. 中国工程物理研究院研究生院，北京10019

雷家睿（2003—），男，四川成都人，北京师范大学物理学系2020级本科生

收稿日期: 2021-12-07

修回日期: 2022-02-21

网络出版日期: 2022-10-26

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Dynamics of a rigid sphere on a rotating annular groove

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1. Department of Physics, Beijing Normal University, Beijing 100875, China;
2. Mingzhang Institution of Xindu No.1 High School，Chengdu 610500，China;
3. Capital Normal University High School，Beijing 100048，China;
4. Graduate School of Chinese Academy of Engineering Physics，Beijing 100084，China

Received date: 2021-12-07

Revised date: 2022-02-21

Online published: 2022-10-26

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摘要

本文研究了刚性球体在绕竖直轴旋转的圆环形槽中的运动情况，发现球体的自转与公转通过摩擦力相互耦合. 理论上，给出了球平衡位置随圆环角速度增加的具体关系，并得到了球在环中具有阻尼振荡特征的动力学行为. 实验上，本文通过3D打印搭建了实验装置，结合所提出的一种测量圆弧面与物体摩擦系数的方法，定量验证了理论的若干预言.

关键词： 刚性球体; 转动圆环; 摩擦力; 动力学过程; IYPT

本文引用格式

雷家睿, 韩润泽, 王柯人, 黄敏, 赵芸赫, 马宇翰 . 刚性球体在转动环形凹槽内的动力学行为[J]. 大学物理, 2022 , 41(10) : 55 . DOI: 10.16854/j.cnki.1000-0712.210605

Abstract

In this paper, the dynamics and trajectory of a rigid sphere in an annular groove rotating around a vertical axis is studied. The rotation and revolution of the sphere are coupled with each other through friction. Theoretically, the balance position of the sphere which monotonically increases with the rotating speed of the annular groove is obtained. And the damped oscillation of the sphere is solved numerically. In addition, an experimental setup is built with the help of 3D printing, and a method is proposed for measuring friction coefficient between the arc surface and the object thereon. The theoretical predictions are quantitatively verified by the experimental results.

Key words： rigid sphere; rotating reference frame; annular groove; friction; dynamic process; IYPT

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